Fountain effect flow front

Correct modeling of the flow near the front of a stream requires a rigorous solution of the hydrodynamic problem with rather complicated boundary conditions at the free surface. In computer modeling of the flow, the method of markers or cells can be used 124 however this method leads to considerable complication the model and a great expenditure of computer time. The model corresponds to the experimental data with acceptable accuracy if the front of the streamis assumed to be flat and the velocity distribution corresponds to fountain flow.125,126 The fountain effect greatly influences the distribution of residence times in a channel and consequently the properties of the reactive medium entering the mold. 

Detailed kinematic investigations of flow near the front of a stream were undertaken.284 A diagram of the experimental device is shown in Fig. 4.49. In the experimental procedure, a liquid was placed in a chamber with transparent walls above an aluminum piston, which was driven downwards by connection to a suitable drive. This resulted in the appearance of streams inside the liquid,and three different flow zones could be distinguished. The so-called "fountain effect discussed in Section 2.11 appeared near the free surface, while a reverse fountain flow was observed below the moving surface. It is interesting to note the movement of two liquids with different densities, when one liquid is used as a piston to push the other (analyzed experimentally and theoretically).285 If the boundary between the two liquids is stationary and the walls of the chamber move at constant velocity, then the pattern of flow is as shown in Fig. 4.50, where flow trajectories corresponding to front and reverse fountain effects are clearly shown. Two other flow patterns -developed flow inside the main part of the chamber and circulation near the surface of the aluminum piston - were also observed. 

The third region of flow near the front is of special interest. The important feature of this region is the fountain effect, which must be considered in modelling all types of mold filling. It is important not only for estimating the hydrodynamic flow pattern, but also because the deformation of the macromolecules near the front influences their orientation and the properties of the end product. 

A simple calculation method, which takes into account the fountain effect, was proposed.289 In this approach the flow is assumed to be laminar and unidimensional. The front of the stream is regarded as straight (plane), perpendicular to the walls of the mold and moving with a constant average velocity vav. Then the following dimensionless variables are introduced ... 

A coordinate of a point, containing liquid moving with velocity vav is designated Zav- As the front line is assumed to be straight, the fountain effect is described by the assumption that transverse flow occurs along this line from the part of the cross-section where the velocity is high... 

The system of equations with initial and boundary conditions formulated above allows us to find the velocity distributions and pressure drop for the filled part of the mold. In order to incorporate effects related to the movement of the stream front and the fountain effect, it is possible to use the velocity distribution obtained285 for isothermal flow of a Newtonian liquid in a semi-infinite plane channel, when the flow is initiated by a piston moving along the channel with velocity uo (it is evident that uo equals the average velocity of the liquid in the channel). An approximate quasi-stationary solution can be found. Introduction of the function v /, transforms the momentum balance equation into a biharmonic equation. Then, after some approximations, the following solution for the function jt was obtained 285... 

Hence, uz -C ux, uy and uz can be ignored. We must point out that this velocity plays a significant role in heat transfer and orientation in the flow front region, because the free flow front is dominated by what is usually referred to as a fountain flow effect. 

Fig. 13.7 Schematic representation of the flow patterns during the filling of an end-gated rectangular mold whose width is much greater than its thickness, (a) Width direction flow fronts at various times, (b) Velocity profiles in the fully developed region, and schematic representation of the fountain effect in the front region.

At the receding side of the moving water front, one can almost always observe small oil droplets dispersed in the water plug as a result of the fountain effect. This effect, which is a consequence of the flow pattern demonstrated in Figure 3, is shown in Figure 7. 

No thermal boundary conditions are required along the edge boundaries in the X -X2 plane due to the neglect of the thermal conduction in the x -X2 plane. The inlet temperature is assumed uniform and taken as the injection melt temperature. The flow-front temperature boundary condition requires a special treatment to mimic the fountain flow effect, which will be discussed later in Chap. 8. 

The flow of the molten or thermally softened polymer mass into the mold cavity is, as previously indicated, a complicated matter. A schematic diagram of the flow pattern is shown in Fig. 8-18. Several aspects of the process merit discussion. First of all, the flow is complicated by the formation of a solidified polymer layer [15-17] at and near the mold wall. Next, the molten or thermally softened polymer flows from the cavity centerline to the front of the mass and then outward toward the wall. This behavior is termed a fountain effect [14,15]. 

For thermosets, the velocity profile of the flow front has been established to be relatively flat and plug-shaped. A thin melt region exists between the charge core and mold surfaces, which ensures that core fluid layers move together in the direction of flow. In the case of thermoplastics, the flow front assumes a more parabolic shape, characteristic of laminar flow. However, due to the fact that solidification initiates in the material in contact with the cooler mold, resin at the core migrates toward the cavity surfaces creating a secondary flow pattern that is known as the fountain flow effect. 

FIGURE 14.26 Tracer patterns near the advancing melt Iront showing the fountain effect for two different initial tracer locations. The rectangular element at the initial melt front gets sheared and extended and reverses direction as material on the flow front gets deposited near the wall. (Data from Coyle, D. J. et al., AIChE J., 33, 1168, 1987. Reprinted by permission of the American Institute of Chemical Engineers.)... 

Fig. 13.18 Predicted velocity field showing fountain flow around the melt front region for non-Newtonian fiber suspension flow at about half the outer radius of the disk. The reference frame is moving with the average velocity of melt front, and the length of arrow is proportional to the magnitude of the velocity. The center corresponds to z/b = 0 and wall is z/b = 1, where z is the direction along the thickness and b is half-gap thickness. [Reprinted by permission from D. H. Chung and T. H. Kwon, Numerical Studies of Fiber Suspensions in an Axisymmetric Radial Diverging Flow The Effects of Modeling and Numerical Assumptions, J. Non-Newt. Fluid Mech., 107, 67-96 (2002).]...

Previous numerical studies have been performed by several authors (Kamal et al. 1986, 1988 Mavridis et al. 1986, 1988 Coyle et al. 1987 Zheng et al. 1990 Jin 1993 Sato and Richardson 1995 Bogaerds et al. 2004 Baltussen et al. 2010 Mitsoulis 2010). These investigations have shown that the fountain flow has significant effects on the melt-front temperature, and also on the molecular or fiber orientation distributions in the skin region near the cavity waU. 

Tadmor [136] used this description to interpret the orientation profile in amorphous polymers (see Fig. 15.33) the orientation in the skin is due to the fountain flow and the secondary maximum to the shear flow behind the front, with, in both cases, some relaxation of the orientation during cooling. This can be generalized to semicrystalline polymers, where the same type of orientation profile is found for the crystalline phase (e.g. [137]), even if it is sometimes difficult to find an orientation maximum at the surface, perhaps for experimental reasons. Additional effects may be introduced by the packing stage. The packing flow may induce a new secondary maximum in the orientation profile, but lower than the first one [137]. 

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